Which of the following numbers is a factor of 189? ${2,3,8,11,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $189$ by each of our answer choices. $189 \div 2 = 94\text{ R }1$ $189 \div 3 = 63$ $189 \div 8 = 23\text{ R }5$ $189 \div 11 = 17\text{ R }2$ $189 \div 14 = 13\text{ R }7$ The only answer choice that divides into $189$ with no remainder is $3$ $ 63$ $3$ $189$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $189$ $189 = 3\times3\times3\times7 3 = 3$ Therefore the only factor of $189$ out of our choices is $3$. We can say that $189$ is divisible by $3$.